He counted Steve Jobs and the early Silicon Valley pack as friends, and happens to be Apple's chairman.
In the early Noughties, Levinson convinced Google co-founder Larry Page to open a company with a blank chequebook and little pressure to return profit.
This company would have one mission: achieve immortality.
On Sept 18 2013, Larry Page wrote to shareholders alerting them that Google had formed a new company focused on "health and well-being [and] the challenge of ageing".
Apple's chief Tim Cook congratulated Art at the time, describing him as "one of the crazy ones", due to his fearless commitment to suspending old age when others scoffed.
Anti-ageing has long been regarded as marketing nonsense, a preserve for cosmetic companies keen to convince women to buy moisturisers.
The cosmetic anti-ageing market was worth US$250 billion ($372.5b) in 2016 and expected to reach US$331.41b by 2021, according to Orbitz Research.
How much could a pill that could stop death in its tracks be worth?
Scientists are coming around to the notion that age can be treated like a disease, rather than an inevitability, and some have suggested we may be able to find a way to switch it off.
The World Health Organisation even added "ageing" to its terminology in February this year.
Calico was one of the first to jump on a trend that has piqued the interest of venture capitalists looking for a new market.
Silicon Valley's elite, who have grown up being taught that everything can be hacked, see no reason the same can't be true of our bodies.
The symptoms of ageing, like white hair and memory loss, are caused by damage to our cells over time as they divide. This constant process starts in the womb but we are able to repair our cells up until about 30. These changes are not consistent among the population.
Some 70-year-olds are weak and frail, while others stay fit. That's what Levinson is interested in.
Calico is looking for the magic pill to cure ageing, thus eliminating the greater risk of conditions that loom larger with age.Some might scoff at a potion to help us live longer.
But scientists have suggested wilder things that turned out to be true. Before Louis Pasteur's germ theory became popular in the 1880s we believed death by disease was bad luck. The discovery of penicillin in 1928 changed that.
So why not imagine a time when we could stop the grip of ageing, offering a better quality of life and relieving pressure on healthcare services?
Since Calico opened its doors five years ago, we have heard little. Its website lists a few studies and research tie-ups.
Last January, it demonstrated that naked mole rats are not more likely to die as they get older.
The bucktoothed mammals are notable for their long lifespans and the research appeared to back up Calico's goal. But no therapies have emerged.
A year after Calico was founded, the company announced a partnership with AbbVie, Chicago-based maker of arthritis drug Humira.
AbbVie was regarded as a hot stock until Pfizer, Amgen and others announced they would launch similar pills.
This summer the partnership was extended, pledging an extra US$500 million each to "discover and bring to market new therapies for patients with age-related diseases".
Calico will be conducting research until 2022 when it will enter "Phase 2a studies" - or as experts have hinted, human testing - and finally the "late-stage development activities".
The pair have agreed to share costs and profit equally. In November it hired Dr Garret FitzGerald, an Irish professor who has been vocal about our "molecular clocks", the idea that genes operate on 24-hour cycles and playing with this can slow down damage.
Rejigging the molecular clock may delay Alzheimer's, he claims. He is one of a number of heavyweights at the company whose leaders include Cynthia Kenyon, Dr David Botstein - chairman of genetics at Stanford University - and Robert Cohen, who joined from Genentech after developing groundbreaking cancer drugs, alongside scientists who use computers to detect complex patterns.
The company has hit some dead ends. In July 2015 Calico signed up to work with AncestryDNA, which makes DNA-testing kits used by millions.
Calico paid for access to pick out families that appeared to live longer, and work out why, but the partnership has ended. Calico made headlines in March when artificial-intelligence expert Daphne Koller quit, the second executive in several months.
Outsiders began to ask what was going on at Calico. The company had no response.
Notoriously closed to outsiders, even workers in the Bay Area's blossoming biotech industry have little idea what its team are up to.
At the same time, other Google spin-offs such as driverless car company Waymo and balloon-internet project Loon are bearing fruit.
Calico's ambition has always been to make people live forever.
Questions about the company's own lifespan remain unanswered.
